Challenge Quizzes

Center of mass of a collection of points

Three particles of respective masses m1=12.0 kg,m_1=12.0\text{ kg},m1​=12.0 kg,m2=25.0 kgm_2=25.0\text{ kg}m2​=25.0 kg and m3=38.0 kgm_3=38.0\text{ kg}m3​=38.0 kg form an equilateral triangle of side length a=140 cm.a=140\text{ cm}.a=140 cm. If we locate m1m_1m1​ at the origin on the xyxyxy-plane, and put m2m_2m2​ to the right of m1m_1m1​ on the xxx-axis, as shown in the above figure, what are the approximate coordinates of the center of mass of this system?

Three particles are on the xyxyxy-plane, as shown in the above figure. The masses of the three particles are m1=2.0 kg,m_1=2.0\text{ kg},m1​=2.0 kg,m2=5.0 kgm_2=5.0\text{ kg}m2​=5.0 kg and m3=9.0 kg.m_3=9.0\text{ kg}.m3​=9.0 kg. If the scales on the axes are set by xs=4.0 mx_s=4.0\text{ m}xs​=4.0 m and ys=6.0 m,y_s=6.0\text{ m},ys​=6.0 m, what are the xyxyxy-coordinates of the system's center of mass?

Consider a uniform bar of length 3L3L3L and mass m3=5m.m_3=5m.m3​=5m. Two balls are hanging on strings with negligible mass from the two ends of the bar, and their masses are m1=mm_1=mm1​=m and m2=3m.m_2=3m.m2​=3m. The lengths of the string on which the balls are hanging are LLL and 2L,2L,2L, respectively, as shown in the above figure. What is the center of mass of this system relative to the midpoint of the bar?

Three particles A,A,A,BBB and CCC are on the xyxyxy-plane. Their masses are mA=2.00 kg,m_A=2.00\text{ kg},mA​=2.00 kg,mB=4.00 kgm_B=4.00\text{ kg}mB​=4.00 kg and mC=3.00 kg,m_C=3.00\text{ kg},mC​=3.00 kg, and the coordinates of AAA and BBB are (−1.40 m,0.48 m)(-1.40\text{ m},0.48\text{ m})(−1.40 m,0.48 m) and (0.70 m,−0.72 m),(0.70\text{ m},-0.72\text{ m}),(0.70 m,−0.72 m), respectively. If the coordinates of the center of mass of the three-particle system is (−0.50 m,−0.70 m),(-0.50\text{ m},-0.70\text{ m}),(−0.50 m,−0.70 m), what is the coordinates of particle C?C ?C?

Three particles of respective masses m1=13.0 kg,m_1=13.0\text{ kg},m1​=13.0 kg,m2=29.0 kgm_2=29.0\text{ kg}m2​=29.0 kg and m3=37.0 kgm_3=37.0\text{ kg}m3​=37.0 kg form an equilateral triangle of side length a=140 cm.a=140\text{ cm}.a=140 cm. If we locate m1m_1m1​ at the origin on the xyxyxy-plane, and put m2m_2m2​ to the right of m1m_1m1​ on the xxx-axis, as shown in the above figure, what are the approximate coordinates of the center of mass of this system?